Recall that the parent Floquet system \({\cal U}=e^{-i\frac{1}{2}{\cal H}_{1}}e^{-i\frac{1}{2}{\cal H}_{2}}\)  possesses multiple and non-Hermiticity induced fourfold degenerate corner modes at zero and \(\pi \)  quasienergies, which are obtained by solving the eigenvalue equation \({\cal U}|\psi \rangle =e^{-iE}|\psi \rangle \) . The numbers of these corner modes are related to a pair of topological
invariants introduced in Ref. [1]}. Since the process of taking
the square (cubic) root of \({\cal U}\)  does not break the protecting
CS of these corner modes, we expect the topological invariants
of \({\cal U}\)  to be able to predict the numbers of corner modes at
the \((0,\pi /2,\pi )\)  [\((0,\pi /3,2\pi /3,\pi )\) ] quasienergies of
\({\cal U}_{1/2}\)  [\({\cal U}_{1/3}\) ].
